Former Chancellor of the Exchequer accepting America's apology (6)
I believe the answer is:
excuse
'apology' is the definition.
(I know that apology can be written as excuse)
'former chancellor of the exchequer accepting america's' is the wordplay.
'former' becomes 'ex' (prefix meaning former or onetime).
'chancellor of the exchequer' becomes 'ce' (I've seen this in other clues).
'accepting' is an insertion indicator (inserted letters are accepted).
'america's' becomes 'US'' ('US' can be a synonym of 'america').
'ce' placed around 'us' is 'cuse'.
'ex'+'cuse'='EXCUSE'
(Other definitions for excuse that I've seen before include "Condone or forgive" , "Supposed reason for failure" , "Grant an exemption or justify" , "Absolve" , "Justifying explanation" .)